Geo 7-2 Similar Polygons
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This document discusses key concepts related to similar polygons including: - Polygons are similar if corresponding angles are congruent and corresponding sides are proportional. - The scale factor is the ratio of corresponding sides in similar figures. - Scale drawings use proportions to relate lengths in a drawing to actual lengths, and are used in applications like poster design.
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440 Chapter 7 SimilaritySimilar Polygons7-2Objective.docx
440 Chapter 7 Similarity
Similar Polygons7-2
Objective To identify and apply similar polygons
A movie theater screen is in the shape of
a rectangle 45 ft wide by 25 ft high.
Which of the TV screen formats at the
right do you think would show the most
complete scene from a movie shown on the
theater screen? Explain.
Similar fi gures have the same shape but not necessarily the same size. You can
abbreviate is similar to with the symbol ,.
Essential Understanding You can use ratios and proportions to decide whether
two polygons are similar and to fi nd unknown side lengths of similar fi gures.
You write a similarity statement with corresponding vertices in order, just as you write
a congruence statement. When three or more ratios are equal, you can write an
extended proportion. Th e proportion ABGH 5
BC
HI 5
CD
IJ 5
AD
GJ is an extended proportion.
A scale factor is the ratio of corresponding linear measurements
of two similar fi gures. Th e ratio of the lengths of corresponding
sides BC and YZ , or more simply stated, the ratio of
corresponding sides, is BCYZ 5
20
8 5
5
2. So the scale factor
of nABC to nXYZ is 52 or 5 : 2.
Key Concept Similar Polygons
Defi ne
Two polygons are
similar polygons if
corresponding angles are
congruent and if the
lengths of corresponding
sides are proportional.
Diagram
ABCD , GHIJ
Symbols
/A > /G
/B > /H
/C > /I
/D > /J
ABGH 5
BC
HI 5
CD
IJ 5
AD
GJ
CB
A D
IH
G J
C X
Y
Z
B
A
ABC XYZ
15 20
25
6 8
10
Dynamic Activity
Similar Polygons
A
C T I V I T I
E S
D
S
AAAAAAAA
C
A
CC
I E
SSSSSSSS
DY
NAMIC
Lesson
Vocabulary
• similar fi gures
• similar polygons
• extended
proportion
• scale factor
• scale drawing
• scale
L
V
L
V
• s
LL
VVV
• s
a
W
r
c
t
You learned about
ratios in the last
lesson. Can you use
ratios to help you
solve the problem?
hsm11gmse_NA_0702.indd 440 4/15/09 1:49:41 PM
http://media.pearsoncmg.com/aw/aw_mml_shared_1/copyright.html
Problem 1
Got It?
Problem 2
Got It?
Lesson 7-2 Similar Polygons 441
Understanding Similarity
kMNP , kSRT
A What are the pairs of congruent angles?
/M > /S, /N > /R, and /P > /T
B What is the extended proportion for the ratios of
corresponding sides?
MNSR 5
NP
RT 5
MP
ST
1. DEFG , HJKL.
a. What are the pairs of congruent angles?
b. What is the extended proportion for the ratios of the lengths of
corresponding sides?
Determining Similarity
Are the polygons similar? If they are, write a similarity statement
and give the scale factor.
A JKLM and TUVW
Step 1 Identify pairs of congruent angles.
/J > /T, /K > /U, /L > /V, and /M > /W
Step 2 Compare the ratios of corresponding sides.
JK
TU 5
12
6 5
2
1
KL
UV 5
24
16 5
3
2
LMVW 5
24
14 5
12
7
JM
TW 5
6
6 5
1
1
Corresponding sides are not proportional, so the polygons are not similar.
B kABC and kEFD
Step 1 Identify pairs of congruent angles.
/A > /D, /B > /E , and /C > /F
Step 2 Compare t.
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440 Chapter 7 SimilaritySimilar Polygons7-2Objective.docx
440 Chapter 7 Similarity
Similar Polygons7-2
Objective To identify and apply similar polygons
A movie theater screen is in the shape of
a rectangle 45 ft wide by 25 ft high.
Which of the TV screen formats at the
right do you think would show the most
complete scene from a movie shown on the
theater screen? Explain.
Similar fi gures have the same shape but not necessarily the same size. You can
abbreviate is similar to with the symbol ,.
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two polygons are similar and to fi nd unknown side lengths of similar fi gures.
You write a similarity statement with corresponding vertices in order, just as you write
a congruence statement. When three or more ratios are equal, you can write an
extended proportion. Th e proportion ABGH 5
BC
HI 5
CD
IJ 5
AD
GJ is an extended proportion.
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of two similar fi gures. Th e ratio of the lengths of corresponding
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corresponding sides, is BCYZ 5
20
8 5
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2. So the scale factor
of nABC to nXYZ is 52 or 5 : 2.
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Defi ne
Two polygons are
similar polygons if
corresponding angles are
congruent and if the
lengths of corresponding
sides are proportional.
Diagram
ABCD , GHIJ
Symbols
/A > /G
/B > /H
/C > /I
/D > /J
ABGH 5
BC
HI 5
CD
IJ 5
AD
GJ
CB
A D
IH
G J
C X
Y
Z
B
A
ABC XYZ
15 20
25
6 8
10
Dynamic Activity
Similar Polygons
A
C T I V I T I
E S
D
S
AAAAAAAA
C
A
CC
I E
SSSSSSSS
DY
NAMIC
Lesson
Vocabulary
• similar fi gures
• similar polygons
• extended
proportion
• scale factor
• scale drawing
• scale
L
V
L
V
• s
LL
VVV
• s
a
W
r
c
t
You learned about
ratios in the last
lesson. Can you use
ratios to help you
solve the problem?
hsm11gmse_NA_0702.indd 440 4/15/09 1:49:41 PM
http://media.pearsoncmg.com/aw/aw_mml_shared_1/copyright.html
Problem 1
Got It?
Problem 2
Got It?
Lesson 7-2 Similar Polygons 441
Understanding Similarity
kMNP , kSRT
A What are the pairs of congruent angles?
/M > /S, /N > /R, and /P > /T
B What is the extended proportion for the ratios of
corresponding sides?
MNSR 5
NP
RT 5
MP
ST
1. DEFG , HJKL.
a. What are the pairs of congruent angles?
b. What is the extended proportion for the ratios of the lengths of
corresponding sides?
Determining Similarity
Are the polygons similar? If they are, write a similarity statement
and give the scale factor.
A JKLM and TUVW
Step 1 Identify pairs of congruent angles.
/J > /T, /K > /U, /L > /V, and /M > /W
Step 2 Compare the ratios of corresponding sides.
JK
TU 5
12
6 5
2
1
KL
UV 5
24
16 5
3
2
LMVW 5
24
14 5
12
7
JM
TW 5
6
6 5
1
1
Corresponding sides are not proportional, so the polygons are not similar.
B kABC and kEFD
Step 1 Identify pairs of congruent angles.
/A > /D, /B > /E , and /C > /F
Step 2 Compare t.
Chapter 1.1
The document discusses properties of similar figures and how to determine if two figures are similar. It provides examples of similar figures and how to use scale factors and proportional sides to determine missing side lengths. Some key points made include:
- Two figures are similar if corresponding angles have the same measure and ratios of corresponding sides are equal.
- The scale factor is the ratio of corresponding sides and can be used to determine unknown side lengths of similar figures.
- Examples show determining if figures are similar and calculating missing side lengths using scale factors and proportional sides.
Text 10.5 similar congruent polygons
Two polygons are similar if they have the same shape but not necessarily the same size. Congruent polygons have the same shape and the same size. The document provides examples of finding corresponding sides and angles of similar and congruent polygons. It also gives examples of determining if two polygons are similar by checking if the ratios of corresponding sides are equal.
Geometry unit 7.2
This document is about similarity and similar polygons from a Holt Geometry textbook. It defines similar polygons as polygons with congruent angles and proportional side lengths. Examples are provided to identify similar polygons and write similarity statements. The similarity ratio of two similar polygons is defined as the ratio of corresponding side lengths. Applications include using proportions to find the length of a model based on its similarity to an actual object.
fjjh
The document defines similar polygons as polygons where corresponding angles are congruent and the ratios of corresponding sides are equal. It provides examples of similar triangles and scale factors. Similar shapes will have congruent corresponding angles and proportional corresponding sides, as demonstrated through examples finding missing side lengths and perimeter ratios of similar polygons.
Hoho
The document provides information on mathematical formulas for calculating the area of squares, rectangles, and triangles as well as the perimeter of polygons. It states that the area of a square can be calculated as s2, where s is the length of one side. The area of a rectangle can be found using the diagonals method, which is half the product of the two equal diagonal lengths. It also provides the formula for calculating the perimeter of a regular polygon as ns, where n is the number of sides and s is the length of one side. Finally, it shares the formula for calculating the area of a triangle using the x and y coordinates of its three vertices.
9 7 perimeters and similarity
This document discusses perimeters and similarity of triangles. It introduces scale factors and explains that if two triangles are similar, then the ratios of their corresponding sides are equal and the ratios of their corresponding perimeters are proportional to the ratios of their corresponding sides. It provides examples of calculating scale factors between similar triangles and using scale factors to determine missing side lengths or perimeters. The document establishes that the ratio found by comparing measures of corresponding sides of similar triangles is called the constant of proportionality or scale factor.
Chapter 6 Section 3 Similar Figures
The document discusses similar figures and scale drawings. It provides examples of using proportions to solve problems involving similar figures, scale drawings, and indirect measurements. Key concepts covered include: similar figures having the same shape but not necessarily the same size, with corresponding angles and sides in proportion; using proportions to solve problems involving similar figures and scale drawings; and using similar triangles to indirectly measure quantities like the height of a tree or flagpole using shadow lengths.
Congr similar
This document defines and provides examples of polygons, congruent polygons, and similar polygons. It begins by defining a polygon as a plane figure with three or more sides, and notes there are different types including convex, concave, and regular polygons. It then defines congruent polygons as having the same size and shape, and similar polygons as having the same shape but different sizes, with corresponding angles and sides that are proportional. Examples are provided to illustrate finding side lengths of similar polygons using size-change factors.
Geom jeopardy ch 8 review
The document discusses similar triangles and proportions. It includes questions about solving proportions, finding similarity ratios, determining if triangles are similar, finding corresponding sides of similar triangles given additional information like areas, and calculating values of variables in proportions involving similar figures.
Chapter 1.2
- Hales, a Greek mathematician, was the first to measure the height of a pyramid using similar triangles. He showed that the ratio of the height of the pyramid to the height of the worker was the same as the ratio of the heights of their respective shadows.
- The document discusses using similar triangles to solve problems involving finding unknown lengths, such as measuring the height of a pyramid based on the shadow lengths of the pyramid and a worker of known height.
- Examples are provided of determining if two triangles are similar based on proportional sides or equal corresponding angles, and using similarities between triangles to find unknown lengths.
Chapter 7
The document provides examples and step-by-step explanations for solving geometry problems involving similar and congruent shapes using transformations and properties of similarity and congruence. In one example, it is determined that two triangles are similar because corresponding angles are congruent. In another example, transformations of a rotation and translation are used to show that two figures are congruent.
Similar triangles
The document discusses similar triangles and how to use proportions to solve problems involving similar triangles. It provides examples of setting up proportions between corresponding sides of similar triangles to determine unknown side lengths. It also gives examples of applying similar triangle proportions to solve real-world problems involving shadows.
2.6.1 Congruent Triangles
Two triangles are congruent if their corresponding angles are equal and their corresponding sides are equal. The order of the vertices in a congruence statement indicates the matching parts between the triangles. If two triangles are congruent, then their corresponding parts will be equal.
Congruent and similar triangle by ritik
This document discusses congruent and similar triangles. It defines that congruent triangles have all sides and angles equal, while similar triangles have the same shape but not necessarily the same size. It explains that two figures can be similar but not congruent, but not the other way around. It then discusses how to determine if triangles are similar using corresponding sides, angles, ratios, and proportions. Specifically, it states that if two triangles have two congruent angles or all sides proportional, then the triangles are similar.
2.7.1 Congruent Triangles
* Write and interpret congruence statements
* Use properties of congruent triangles
* Prove triangles congruent using the definition of congruence
Ratios, proportions, similar figures
1) Ratios and proportions are used in many areas including map reading, scale drawings, and solving problems.
2) A ratio compares two quantities by division, and ratios that make the same comparison are equivalent ratios. Proportions are equations that state two ratios are equal.
3) Similar figures have the same shape but not necessarily the same size, with corresponding angles being congruent and corresponding sides forming equivalent ratios. Ratios and proportions can be used to solve for unknown sides or quantities in similar figures.
classification of quadrilaterals grade 9.pptx
This document defines and compares different types of quadrilaterals: parallelograms, rhombi, rectangles, squares, trapezoids, and kites. It provides properties and examples of each shape. Key points include: a parallelogram has two pairs of parallel opposite sides; a rhombus is a parallelogram with four congruent sides; a rectangle is a parallelogram with four right angles; a square has properties of both a rectangle and rhombus; a trapezoid has at least one pair of parallel sides; and a kite has two pairs of congruent consecutive sides. The document also covers angle sums, using properties to solve problems, and includes a logo
Ratios and Proportions.pptx
This document discusses ratios, proportions, and their uses. It provides examples of ratios comparing quantities like shaded area to unshaded area in rectangles. Proportions are defined as ratios that are equal, such as fractions that reduce to the same value. Examples are given for solving proportions to find unknown values. Similar figures are discussed as having the same shape but not necessarily the same size, with corresponding angles being congruent and sides proportional. Methods are presented for using proportions to solve for unknown sides or values in similar or scaled figures.
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- 2. Students will be able to identify and apply similar polygons
- 3. You can use ratios and proportions to decide whether two polygons are similar and to find unknown side lengths of similar figures.
- 4. Have the same shape but not necessarily the same size Is similar to is abbreviated by ~ symbol Two Polygons are similar if corresponding angles are congruent and the corresponding sides are proportional
- 5. Like congruence statements, the order matters so if two figures are similar, their corresponding parts should be in the same order If ΔABC ~ ΔDEG then <A ≅ <D and AB ~ DE
- 6. Use when three or more ratios are equal AB = BC = CD = AD GH HI IJ GJ Scale Factor: ratio of corresponding linear measurements to two similar figures (ratio of corresponding sides in simplest form)
- 7. What are the pairs of congruent angles if ΔABC ~ ΔRST? What is the extended proportion for the ratios of corresponding sides for ΔABC ~ ΔRST?
- 11. ABCD ~ EFGD What is the value of x? What is the value of y?
- 13. Your class is making a poster for a rally. The poster’s design is 6in. high by 10 in. wide. The space allowed for the poster is 4 ft high by 8ft wide. What are the dimensions for the largest poster that will fit in the space? What if the dimensions of the largest space was 3 ft high by 4 ft wide?
- 15. All lengths are proportional to their corresponding actual lengths Scale: ratio that compares each length in the scale drawing to the actual length Where have you seen a scale?
- 16. The diagram shows a scale drawing of the Golden Gate Bridge. The distance between the two towers is the main span. What is the actual length of the main span of the bridge if it is 6.4 cm in the drawing?
- 17. Pg. 375 # 1 – 18, 21 – 28, 32 27 Problems